5. (a) show that (( yp(y))-> using derivatives.
(b) show that (x)(H(x)->A(x))->( [(y)H(y)
N(x,y)->(Y)(A(y)N(x,y))] is logically valid statement.
6. (a) show that f(x,y)=xy is primitive recursive function.
(b) show that the function f(x,y)=x-y is partial recursive.
7. (a) let [ ] be the greatest integer show that [.
(b) show that the set of divisors of a positive integers is recursive.
8. (a) if si ≡sj then for any input sequence (six)≡(sj,x).
(b). construct turing machine that will compute f<x,y> where f is (i) multiplication (ii)|x-y|.